North Yorkshire County Council says it has found a preferred bidder to carry out the delayed project which will see a new carriageway built for the A59 at Kex Gill.
The road is a key east-west link for the county and has been hit by 12 landslides in as many years, leading to diversions for motorists and costs for the council.
In one instance, a landslide in January 2016 shut the road for eight weeks.
The council had hoped works would start last autumn, however, the project has been hit by several delays including objections to compulsory purchase orders which the council made to acquire land for the new route.
Minerals company Sibelco also attempted to call in the project for a public inquiry, but this was rejected by the government.
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There is now an aim for construction to begin next January, with completion in early 2025.
Funding for the project is coming from the Department of Transport which has agreed to provide £56 million, while the council will make up the rest of the costs.
The council's executive will be asked to agree to the awarding of the contract to the preferred bidder at a meeting next Tuesday.
But before the contract can be signed off, a final business case for the project will be submitted to the Department for Transport.
A report to Tuesday's meeting said the road was still causing repair costs for the council which has planned drainage works this month and wants to see a permanent solution in place.
The report said: "There remains a high risk that there will be further landslips in the future, which could potentially result in long term closures of the route, severely impacting connectivity between Skipton and Harrogate.
"Conversely there is a risk to public safety and economic disruption.
"Whilst short to medium term management measures are continually being undertaken, the county council recognised that in the longer term there was a need to develop proposals for a permanent solution."
By Jacob Webster, Local Democracy Reporter